To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary

Received: 5-Feb-01
Accepted: 15-Aug-01
Published: 31-Oct-01

Abstract

This article presents a model of the structure of the information flows that underlie the creation of production chains between thousands of small textile firms located in Prato, central Italy. Contrary to most textile industry of western Europe and north America, Prato did not die out once average salaries in the region rose towards the world's highest. The reason is that Prato was able to switch from a competitive advantage based on low prices to a competitive advantage based on the aesthetical features and variety of textiles. Analysis of the structure of production chains can explain the performance of this distributed production system throughout its evolution. The model reconstructs interactions of ten types of Pratese firms from 1946 to 1993 on a scale of 1:1.

Keywords:

Prato, Industrial Districts, Distributed Intelligence

Introduction

It often happens that firms operating in the same industry are also geographically clustered, but, in many or possibly most cases, physical proximity does not affect firms' individualistic behaviour. On the contrary, in some cases firms that are close to one another and operate in the same industry entertain complex and variable relationships of competition and collaboration with one another, ranging from formal subcontracting to informal communications that foster innovation and entrepreneurship. Alfred Marshall first pointed to the peculiar "industrial atmosphere" of certain clusters, pointing to Sheffield's cutlery industry in the nineteenth century as a prototypical example of this peculiar industrial organisation (Marshall, 1920). Following Marshall, industrial clusters where the structure of interactions matters for aggregate outcome are called industrial districts.

Until the last two decades of the twentieth century, mass production of standardised goods generally called for large, vertically integrated Fordist firms. Consequently, common wisdom among economists was that economic development necessarily follows a path that leads to ever larger firms. According to the view prevailing at that time, industrial districts can only be found in the early stages of economic development.

However, just in the typically Fordist decades after World War II a large part of Italy was providing an exception to this paradigm. Giacomo Becattini first noted that, besides the heavy industrialised North-West and the depressed South, a "third Italy" was growing in the Center-North and North-East areas, one which based economic development on a huge number of small, family-owned firms (Becattini 1969, Becattini 1975). Becattini based his considerations on Tuscany, particularly on a textile district located in Prato, near Florence. With its thousands of firms, mostly very small and specialised in a single production phase, Prato became the prototypical Italianate industrial district.

Industrial districts became fashionable but, possibly, in the wrong way. Less than twenty years after their discovery, some scholars had to remark that during the 1980s industrial districts had become an opposite, equally arbitrary view of economic development based on small-scale capitalism, collaboration and harmony (Amin and Robins 1990; Amin and Thrift 1992). Sharing their critical but constructive attitude, several field studies questioned the realism of this idealised picture. On the one hand, a number of empirical investigations highlighted the importance of hierarchical structures within industrial districts, in Italy and elsewhere (Scott 1992; Gray, Golob, Markusen and Park 1998; Lazerson and Lorenzoni 1999; Rabellotti and Schmitz 1999). On the other hand, other authors pointed to low wages, workers exploitation and poor environmental controls in small firms as a key determinant for the economic success of industrial districts (Harrison 1994; De Cecco 2000) while, at least in Italy, the conflict-composing force of family ties is fading away (Pietrobelli 1998).

In short, industrial districts are interesting because they seem to be an instance of the idea that "the whole is more than the sum of its parts". However, one may suspect that a grim reality of poverty and exploitation hides behind the facade. Prato is an ideal place to assess the relative weight of these interpretations, and not only because it is the very place that initiated modern theorising on industrial districts.

In Prato, a textile manufacturing tradition goes back to the Middle Ages. Industrialisation came at the end of the nineteenth century, when a few large woollen mills joined a long-standing craft tradition of independent weavers and warpers. Prato maintained this structure until the end of World War II: until this time, one cannot speak of a Marshallian industrial district with its "industrial atmosphere".

The economic crisis ensuing the end of World War II was the event that marked the beginning of the most famous Italian industrial districts (Cioni 1997). In a situation of extreme poverty, with woollen mills shutting down or resizing their productive capacity, young members of large extended families devoted to commerce or agriculture started to integrate their income with some irregular work at the loom, for which they could eventually mobilise their whole family just as they used to do at harvest times. Another source of independent firms was provided directly by the large woollen mills, particularly during the 1949 crisis. Simply, managers offered workers the options of either buying or renting looms or other machinery and being contracted at demand peaks, or being fired. Many workers, particularly those who could set a large family to work, found it a good deal.

In both cases, self-exploitation of one's own family members was determinant for the profitability of these minuscule firms. Actually, many among the many thousands of independent firms in the district should be rather called "precarious workers".[1] Given the importance of self-exploitation for the Pratese economy, my question is: What happened in the subsequent decades, when salaries rose and people could find better jobs? Why does Prato still exist as an industrial district?

A first answer is that, due to massive clandestine immigration, Prato can still rely on a cheap labour force. Exploitation and self-exploitation never ended, and possibly increased because nowadays many workers do not have any legal right whatsoever, not even permission to stay in Italy. Interestingly, most foreign immigrants are Chineses coming from the Zhejiang province, where a socks and stockings district based on small family firms is flourishing on similar lines as in Prato (Wang, Zhu and Tong 2001).

Clearly, quantifying clandestine immigration is impossible if one only looks at official statistics. However, a rough estimate can be provided by Caritas, the Catholic agency for the poor. In fact, in 1995 and 1998 the State offered legalisation to clandestine immigrants who could demonstrate that they had been living and working in Italy for a certain number of years. Obviously, such a certification could not be provided by the firms for which these people worked illegally. On the contrary, Caritas could provide such a certification if a clandestine immigrate had registered early enough with it. Since 1988, Pratese Caritas has collected data on clandestine immigrants who ask to be registered in their files, as well as the number of those who made use of the two legalisations in 1995 and 1998.

Figure 1 shows clandestine immigrants according to Caritas data (red line), net of legalisations in 1995 and 1998. Furthermore, official statistics on foreign residents have been added (blue line).

Figure 1. The red line shows clandestine immigrants in Prato according to Caritas files, net of legalisations in 1995 and 1998 (Caritas 2000). Although Caritas started to collect data in 1988, no clandestine was recorded in 1988 and 1989. The blue line shows foreign residents in the Prato province, 1995 to 1999 (ISTAT 2000). Foreign residents in the previous years have been guessed by subtracting from foreign residents in 1995 the net inflow to Prato from abroad (ISTAT 1990-1994). Clearly, this estimate is reliable only to the extent that net flows from abroad are constituted by foreign citizens, that net flows of foreign citizens between Prato and other Italian provinces are negligible, and that among foreigners deaths compensate births.

Clearly, only a fraction of illegal workers resorts to Caritas so the above is likely to be a cautious estimate, particularly for early years when rumours about the possibility of legalisations were not widespread and the role of Caritas was not clear. Even with these data, clandestine immigrants are about one third of legally resident foreigners, which is sufficient to have an impact on real labour costs. This impression is confirmed by data on the inspections carried out by the Italian agency for labour safety (INPS), where Prato stays on top of illegal labour in Tuscany (Baccini, Castellucci, Mori and Vasta 2001).

However, availability of cheap labour is not sufficient to explain Prato's puzzle. After all, moving a plant or subcontracting abroad is easier than relying on clandestine workers whose presence exposes firms to rackets of any sort. If self-exploitation would be the only determinant of Prato's economic success, then why not just move production abroad when labour cost increases? Most textile districts in Western Europe and North America did so. Why did not Prato?

Actually, there has been a time where this seemed to be Prato's fate as well. As we have seen, the district originated in the early 1950s, gained momentum at the beginning of the 1960s and continued to expand throughout the 1960s and 1970s. However, at the beginning of the 1980s a deep crisis struck Prato. Experts had good reason to claim that textile production was no longer feasible in a region where income had been raised to the world's highest standards, and that textile production would move away. Figure 2 illustrates this development in terms of production plants and number of workers (official statistics).

Surprisingly, the predictions were not fulfilled. Contrary to all expectations, Prato managed to recover during the 1990s. Recovery is not evident from figures 2a and 2b, which only point to industry concentration in the first half of the 1990s, but it is evident to all local operators (Balestri and Toccafondi 1994, Balestri and Toccafondi 1995).

However, Prato is now a very different district from the one that existed in the 1960s and 1970s. It is less typical a district, both because some concentration did take place and because it is no longer a self-contained productive area. Most importantly, Prato switched from a competitive advantage based on price to a competitive advantage based on taste and product variety: I claim that here lies the reason of its unexpected recovery.

Since these qualities are deeply embedded in the local culture, workers had to move from low-wage countries to Prato instead of plants moving from Prato to low-wage countries. Note that, from this point of view, Prato is actually even more a Marshallian district today than it used to be in the 1960s and 1970s. Today more than ever, its competitive advantage relies on local culture, tradition or, to speak in Marshall's terms, "atmosphere".

This article aims to disentangle the role of price-based competitive advantage from variety-based competitive advantage, from the end of World War II to the beginning of the recovery of the 1990s. It does so by means of a model of interacting firms, in the conviction that different sources of competitive advantage reflect different business relationships. In particular, Section 2 explains the influence of single production phases on different sources of competitive advantage, Section 3 illustrates the structure of information flows within the district, and Section 4 presents the model. Finally, Section 5 illustrates the results of the model and Section 6 concludes.

From Price Flexibility to feature flexibility

Traditionally, Prato used to produce low-quality, low-price textiles out of regenerated wool. Regenerated wool is obtained from used clothes and woollen rags of almost any sort, after a series of chemical and mechanical processes that yield less resistant, rougher fabrics than virgin wool.

Of the two spinning methods - carded spinning and combed spinning - only the first can be used with regenerated wool. However, identifying carded fabrics with lower-quality fabrics would be a mistake, since quality rather depends on raw materials and processing details. Today, wool regeneration has almost disappeared from Prato, average quality is much higher than it used to be, but still, for historical reasons, most Pratese firms are focused on carded fabrics.

Figure 3 illustrates a general scheme of the production process to be found in Prato (Avigdor 1961). Wool (either virgin or regenerated) must be spun (either carded or combed), warped and then woven. Dyeing can either take place before spinning, or between spinning and warping, or after weaving. Finally, fabrics receive a final touch with finishing operations. Since technical innovations either concern machinery or details that at this level of generality do not show up, we can safely assume that this scheme did not change.

Figure 3. A scheme of the production process to be found in Prato, rough enough to be considered constant over time. Dyeing can either take place before spinning, or before warping, or just before finishing operations.

Throughout the "Golden Age" of the 1960s and 1970s and well into the 1980s, most Pratese firms relied on regenerated wool, low quality and low price. With its huge number of small firms doing the same things, the district worked nearly like a textbook competitive economy where profits tend to zero.

For many years, the district organisation discouraged technological innovation (Bertini and Forlai 1989). On the one hand textile technology poses very low barriers to entry, because if the only difference between current generation looms and previous-generation looms is speed, then one can easily enter the market by purchasing a second-hand loom and working harder than competitors. On the other hand, once a worker has become independent, dedicated skills, personal pride and, most importantly, a lack of alternative jobs that are not related to the textile industry and move countercyclically to its ups and downs, erect terrible barriers to exit. Thus, investment in technological excellence was discouraged, since if a firm did that, it had to face price competition by a number of craftsmen in despair.

While the above is absolutely true for the first stages of the production process, it becomes the less true the further we move towards the final product (Aiazzi, Baussola, Corsini, Ganugi and Langianni 1997). Rags are all alike and weaving is all alike as well, but dyeing and, to a greater extent, finishing offers a wider range of possibilities to differentiate products. Particularly during the 1990s, the range of finishing operations increased enormously, offering tremendous possibilities for differentiating final products (Bonafé, Giusti, Limberti, Ponzecchi, Romagnoli and Terenzi 1999).

Building on a sense of aesthetical inventiveness within a classical taste that is typical of Tuscany, Pratese firms aimed to differentiate final products. Quantitative estimates do not exist, but according to the Prato industrialists' union's chief researcher, Andrea Balestri (2000), product differentiation started in the 1970s, accelerated in the 1980s and has continued to grow exponentially ever since.

According to a survey carried out among customers in 1990, Prato is basing its competitive advantage on its ability to provide anything a buyer may request, in a reasonable time, in lots of any size and with great creativity and taste (Balestri and Toccafondi 1991). Low price comes last.

Thus, by looking at firms that operate at different levels of the productive process we can distinguish price-based competitive advantage from variety-based competitive advantage. In both cases, the district attains flexibility by means of massive interactions of a huge number of firms. However, in the first case interactions take place pretty much in the way neoclassical economics describes them, so the district attains price flexibility. In contrast, in the second case interactions serve the purpose of stimulating the ability to innovate by creating fabrics with novel features (Lane and Maxfield 1996; Maskell 2000). I call this feature flexibility.

This is the key observation for building the model that will be presented in the following section, which aims to assess the relative importance of price flexibility and feature flexibility. Notably, both price flexibility and feature flexibility run contrary to the prescription of establishing stable inter-firm relationships in order to attain higher qualitative standards.

This is a widespread trend today. Originating from observation of the superior performance of the Toyota manufacturing system in the 1980s, it rapidly diffused across industries and countries. Allegedly, risk-sharing and joint product development are important in order to enhance quality.

Although it was conceived as a means to manage relationships between a large corporation and its main subcontractors, the practice of relying on long-term collaboration bears on industrial districts as well, particularly if they rely on high-quality products (Nuti and Cainelli 1996). Prato is relying more on variety than qualitative excellence; nonetheless, quality is a much-debated issue among local operators. Traditionally, widespread subcontracting poses the following two problems with respect to quality standards:

Poor constancy of whatever quality level is requested by the customer, since a single customer may receive lots that have been processed by different firms;

Free-riding, if poor quality on a production phase reduces the costs of the firm that carries it out but increases the costs of the firm that carries out the subsequent phase (Bertini and Forlai 1989).

In order to overcome these problems, some scholars are pleading for more stable customer-supplier relationships according to the Toyota model (Ciappei and Neri 1998). However, the local chamber of commerce is attempting to pursue an alternative strategy, based on a quality certification that entails checks of all steps of the production process across different firms (Baldini and Tesi 1996). According to this view, quality certification by a State agency could improve quality without impairing the flexibility upon which Prato based its competitive advantage.

Lack of data forces the model presented here to stop at the very beginning of the 1990s. Up to that time, increasing stability of customer-supplier relationships can be assumed not to be a relevant issue in Prato; however, it might undermine the application of this model to a subsequent period.

The Structure of Information Flows

The striking feature of industrial districts is that their macroscopic behaviour exhibits features that its component firms do not have, since they derive from the structure of interactions between component firms. Differently from most economic theory and practice, the macroscopic behaviour of industrial districts cannot be derived from summation of the behaviours of single firms.

If industrial districts are organisms rather than collections of isolated agents, then it is quite natural to stress their similarity with self-organising systems in physics and biology (Biggiero 2001). Particularly, brains are a very interesting class of self-organising systems since distributed memory and knowledge arise out of the structure of interactions between neurones. Thus, several authors have pointed to the possibility of highlighting the "collective mind" of a district by viewing it as a self-organising system (Rullani 1993; Grandinetti and Rullani 1994; Lombardi 2000, Lombardi 2001).

This idea does make sense but - at least in respect of Prato - it needs some qualification. Self-organisation may take place in systems that are constituted by a large number of interacting parts, if patterns of interactions are such that a macroscopic input is able to trigger the formation of microscopic structures. In physics, the simplest examples of a self-organising system are Bénard cells (Nicolis and Prigogine 1977, Nicolis and Prigogine 1989; Haken 1983, Haken 1987): if one heats a pan filled with water from below, one observes the formation of cells where water circulates from the heated bottom to the cool surface and back. Interestingly, this is a microscopic structure that has been created by a macroscopic input (the heat), not by microscopic command by single water molecules. In biology, life itself is a self-organising system (Varela 1979; Rosen 1991), since it consists of an organism's ability to re-produce the code and conditions that generated itself. In essence, life is a logical circuit at the microscopic level that is supported by macroscopic flows of matter and energy. Finally, distributed, self-organising memories in human brains and artificial neural nets are based on information circuits (Kohonen 1989). The idea of a distributed memory is that information is not stored in any particular neurone, but in the circuits where it flows within the system. Just like any self-organising system, a distributed memory is made by a net of microscopic links that can form themselves because of macroscopic conditions in terms of blood flows or electrical current, in the case of artificial neural nets.

Strictly speaking, the idea of circuit, or feed-back, is not necessary in order to have self-organisation. In fact, one could think of a system where macroscopic stimuli trigger the generation of stars, or hierarchies, or any other structure. For instance, von Foerster's famous example of a number of little magnets that join into complex architectures is one where self-organisation does not produce circuits (von Foerster 1982). However, from the above discussion it is clear that self-organising systems where circuits arise are by far the most interesting ones, to the point that self-organisation is generally thought of in connection with this structure.

Admittedly, viewing an industrial district as a self-organising system is an intriguing idea. It means that each particular district has certain ways of organising information flows that make it responsive to particular patterns of demand or to particular technologies. However, a district that is able to form stable information circuits would be one that has a collective behaviour of which its component firms are not even conscious.

Let us examine this case more carefully. A textile district that behaves like that would be one where a multitude of small producers weave and warp according to individual convenience, until fabrics come out that nobody designed, nobody ordered but, miraculously, in the end somebody buys. Prato is not like that, and I wonder if any district has ever been. Nonetheless, certain forms of self-organisation do take place.

In Prato, technical information, financial information and commercial information flow according to very different patterns. Information regarding technical innovations cannot be kept secret in Prato. Frequent subcontracting, workers' mobility and the very fact that the technical innovations made in Prato are incremental and can be easily adopted, are all factors that make technical information spread very rapidly throughout the district. We can think of irregular and provisional information structures of any kind, including circuits, though possibly not stable enough to characterise the macroscopic behaviour of the district. As regards financial information, little or nothing is known. We know that family ties are important for financing the smallest firms, we know that local credit institutes have specific acquaintances and knowledge and we suspect that firm-to-firm loans take place as well, but we have no information concerning the structure of all these loans. However, we know the structure of commercial information. Commercial information flows according to a pattern that corresponds to the organisation of production in the district.

In Prato, production is organised by a special class of agents, herein called the middlemen (Bertini and Forlai 1989). A middleman can either be one of the large woollen mills, or a much smaller firm eventually composed only of a manager, a secretary and a telephone.[2] Contrary to many other Pratese firms, middlemen have entrepreneurial spirit, make strategic plans and are acquainted with the fashion industry.

Whoever wants to buy in Prato, asks a middleman. If the order exceeds its productive capacity, the middleman calls several small firms in order to carry out specific production phases. Wares do not even need to pass physically through the middleman's workshop, but the sequencing of operations is up to the middleman.

For a middleman, nothing is more crucial than that the identity of the final buyer remains secret to the firms that he contracts. Otherwise, these firms could possibly sell directly to the final buyer, or become middlemen themselves. Obviously, this does not amount to claiming that middlemen do not rely on communication, organisation and networking skills. However, keeping the secrecy of private information is part of their job.

If a firm that has been contracted by a middleman is not able to fulfil the whole order with its productive capacity, it will contract another firm in its turn. Thus, the contracted firm takes the middleman role with respect to the firm that it contracts in its turn. This means that, at least in principle, the information structure of subcontracting can repeat itself over and over, like a fractal.

Clearly, this structure of information flows does not produce information circuits. It is a hierarchical information structure, where middlemen have the power to direct information flows. However, note that at the lowest levels this structure in not a single-hierarchy but rather a multi-hierarchy, since it may happen that firm A contracts firm B and, at a later time, firm B contracts firm A. In this sense, but only in this sense, it can be claimed that reciprocity and collaboration are widespread in the district.

The Model

The model aims to reconstruct the structure of business relationships between Pratese firms throughout the evolution of the industrial district, looking for a connection between the structure of business relationships and the historical performance of the district as it was outlined in the introduction. Clearly, the extent to which this can be done depends on the amount of information that we have regarding business relationships within the district.

Although we know the structure of subcontracting, we do not have any data concerning exchanges between firms within the district, either in money terms or in physical magnitude. Similarly, data concerning the size of firms are either fragmentary or too aggregate. The only disaggregated data about the number of firms operating in 56 distinct production phases from 1946 to 1993, was collected by Luciana Lazzeretti and Dimitri Storai (Lazzeretti and Storai 1999). Unfortunately, the numerical content of this database is not accessible, although a visual guess of the graphs entailed in the this publication could be made.

Thus, a very crude assumption has to be made in order to let a model run. The assumption is that small firms process smaller lots than large firms, and that firm size and lot size are perfectly related. If this assumption holds, then the number of orders that firms place on one another is independent of their size.

Furthermore, in order to keep the model tractable, only 10 out of the 56 types of firms considered by Lazzeretti and Storai have been included in the model. Firstly, firms that do not participate in the production processes illustrated in figure 3 have been excluded. Secondly, in order to curb the impact of the above assumption on lot sizes compensating firm size, large woollen mills that occasionally act as middlemen have been excluded as well. Finally, firms showing the most diverse population dynamics have been selected in order not to have redundant information. Ultimately, the ten types of firms that have been considered are: Traders of Raw Materials, Rag Collectors, Carded Spinners, Combed Spinners, Warpers, Weavers, Dyeing Plants, Finishers, Traders of Finished Products and Middlemen.

Finally, since we neither know the geographical locations of firms nor the informal networks of entrepreneurs, we cannot reproduce preferential interactions between firms. Thus, firms can only be distributed uniformly in a space that represents acquaintance proximity.

Of the above limitations, (1) is the least serious and (2) the most serious, but (3) and (4) affect the outcome as well. Unfortunately, there is no way to test for their influence on the model except from ex post observation of its results. However, one should keep in mind that this model was not conceived in order to make numerical forecasts but in order to better understand the historical performance of the district.

The model reproduces the information structure described in Section 3. Firms are represented by coloured squares on a black display. Firms move on the display, forming production chains that appear as multi-coloured stripes. Figure 4 illustrates the correspondence between firm type and the colour of the square that represents it. Figure 5 shows a typical simulation step, with isolated firms and production chains.

Figure 4. Correspondence between colours and types of firms. Whenever possible, warm, pale colours have been used to represent early stages of the production process, cool, dark colours to represent end stages.

Figure 5. A typical simulation step, chosen from the final part of the time period in order to have a large number of firms and production chains of different shapes. This picture stems from a run of the 1:10 model.

Firms numbers are available in 1:1, 1:2 and 1:10 scale. Since scaling affects the results of the model, 1:1 scaling should be used in order to derive realistic values. However, 1:10 scaling makes sense if we want to see a clear picture of the formation of production chains. The advantages and drawbacks of 1:2 scaling lie in between.

Each year is subdivided into steps. At each step, firms interact. In order to obtain smooth results, the number of interactions should be approximately the same every year. However, since the number of firms is different every year, the number of steps should not be the same every year. Consequently, the number of steps is found by requiring that the product of the number of steps and the number of firms is constant.

At each step, all firms except middlemen make a random move in the area. In particular, traders of finished products look for a middleman. As soon as they detect a middleman in their watching range, and after checking that at least one of its four sides is free, they move there and place an order. Theoretically, the fact that middlemen can only create up to four production chains at a time is an unjustified assumption. In practice, on an average of ten simulations the fraction of times where a middleman built four chains was less than 0.2%, so if five or more chains could be built, the results would not change much.

At this point, the middleman looks around for suitable firms in order to build a production chain. Middlemen arrange firms into sequences that respect the technological constraints illustrated in figure 3 (Avigdor 1961). Given the 10 types of firms that we are considering, technological constraints restrict the set of possibilities to the 11 production chains illustrated in figure 6.

Production chains may vary from one another because some production factors can be either produced within the district or purchased outside, because spinning can be either carded or combed, and because dyeing can take place at different production stages. Nonetheless, all production chains must begin with a trader of finished products and end with a trader of raw materials.

Figure 7 illustrates production chains that vary from one another because of the sequencing of operations, because they make use of carded or combed spinning, and because intermediate products are purchased outside the district. In this latter case, production chains are shorter.

Figure 7. Four examples of production chains. Chain A consists of buying wool, combed spinning, dyeing, warping, weaving, finishing and selling fabrics. Chain B differs from chain A because it makes use of carded spinning, rather than combed spinning. Chain C differs from chain B only because dyeing takes place at a later stage. Finally, chain D differs from chain C because yarn is purchased outside the district.

In order to arrange a production chain, a middleman looks first for a firm that can be added to a trader of finished products, that must be a finisher according to figure 6. As soon as the middleman has found a finisher, he attaches it to the trader of finished products. Then the middleman looks for a firm that can be added to the finisher, that according to figure 6 can either be a weaver or a dyeing plant. And so on, until a trader of raw materials is found and the production chain has been completed.

Thus, selection of one of the eleven possible production chains depends on which firms are nearest to the middleman. Implicitly, this model assumes that the empirically given number of firms subsumes all microeconomic variables that determine exchanges. In other words, it assumes economic equilibrium through firms' reproduction and selection and reconstructs the structure of information flows for any given equilibrium state.

At the end of each step, all production chains are destroyed and component firms are set free. However, if the trader of finished products remains close enough to the middleman, the next step it will prompt the construction of a production chain attached at the same side of the same middleman. Thus, when looking at the simulation one may have the impression that some production chains stay there for quite a long time.

However, the reconstructed chain is not necessarily identical with the previous one. Firstly, because component firms may have changed even if their type did not. Secondly, because dyeing plants can be placed at different points of a production chain. In this latter case, we may see a production chain staying there except for some coloured squares exchanging their places.

Even without running the model, construction and destruction of production chains can be seen in a movie of the last four simulation years (Animation 1). Production chains occasionally take weird shapes in order to avoid locations where other firms are present without impairing the results of the simulation. Consider that since the simulation refers to information exchange, not production, it is not unrealistic to see many idle firms at a time.

Animation 1. [To restart the animation, click on the image and select Reload from the right button menu]

Once the model is set up, our task is that of identifying magnitudes that link the structure of information flows to price flexibility and feature flexibility. The next section derives a few indicators of Prato information structure and compares them with the historical development of this industrial district.

The Indicators

Indicators should reflect the flexibility of the district, in terms of price as well as in terms of the qualitative features of fabrics. Both price and feature flexibility depend on the availability of a wide range of possibilities for building production chains. In fact, the availability of a large number of firms in a large number of types enables middlemen to change the firms that they contract with frequently.

Thus, we can measure flexibility by means of an index of the variability of the production chains that are built in the district. The more variable production chains are, the more flexible is the district both in terms of price and features of its products.

However, if the number of types of firms is given and the number of firms is increasing, then an increasing number of firms will be arranged into identical production chains at any given point in time. This results in increasing parallelism of information processing, meaning that at each step there will be several identical production chains.

Although a certain degree of parallelism may contribute to the flexibility of the district, too high a parallelism indicates that the overall volume of orders is large enough for production to be organised more efficiently by larger firms. Thus, it is convenient to use parallelism as a second indicator of the overall performance of the district.

Variability is computed as follows. At each time step, the program records which production chains are built and to which side of which middleman they are attached. During each year, the program compares the chains that are built in the current step with the chains that were built in the previous step. Every time that a production chain is found attached to the same side of the same middleman as in the previous step, a variable constancy is incremented. Subsequently, a degreeOfVariability is defined as one minus the ratio of constancy to the number of chains that have been built during the current step. A summedDegreeOfVariability sums the degreeOfVariability over a year. Finally, variability during one year is obtained by dividing summedDegreeOfVariability by the number of steps in that year.

Parallelism is computed as follows. At each time step, the program records which production chains are built. At the end of the step, the program checks whether a chain X appeared at least twice. If this occurred, a variable chainXParallelism is set equal to the number of chains X that have been built. Subsequently, these variables are averaged over all chains in order to yield a degreeOfParallelism. This degreeOfParallelism is added to a summedDegreeOfParallelism. Finally, at the end of each year parallelism is obtained by dividing summedDegreeOfParallelism by the number of steps in that year.

Figure 8 depicts variability and parallelism calculated by the 1:1 model and averaged over ten runs. Parameters are the variance of the normal distribution that regulates the movements of traders of finished products, their watching range, and the size of the world where firms move.

Figure 8. Variability and parallelism averaged over ten runs. Scale of the simulations: 1:1. Variance of the distribution that regulates the movements of traders of finished products: 10.0. Watching range of traders of finished products: 10x10 pixels. World size: 500x600 pixels.

In figure 8 we see variability increasing continuously from the end of the 1950s, when the Prato industrial district began to expand, to the end of the 1970s, shortly before the crisis began. In contrast, parallelism was very low until mid 1970s, when it started to increase very rapidly. Since the early 1980s, parallelism is increasing and variability is decreasing.

Thus, it appears that the Golden Age of the 1960s and 1970s corresponds to a combination of high variability and low parallelism. Apparently, the Golden Age was characterised by extremely frequent exchange of the firms contracted by middlemen, probably reflecting harsh price competition, together with a high differentiation of production chains, indicating that large, integrated firms had a hard time to carry out the same jobs.

Since the 1980s Prato has exhibited slightly decreasing variability and ever increasing parallelism. Thus, it appears that business relations are becoming a slightly more stable and also that more and more middlemen are doing the same thing at a time, suggesting that industry concentration should take place. It actually did, as from figure 2 it is evident that in the 1990s the number of plants is decreasing although occupation is stable.

The shift from price flexibility to feature flexibility is not captured by the above curves because they do not distinguish among contributions by different types of firms. Feature flexibility is not attained uniformly along the production process, but rather at the very end. The earlier stages of the production process remained largely unaffected by the historical shift from a competitive advantage based on low prices to a competitive advantage based on fabric variety.

Thus, finishers are the natural candidates for highlighting feature flexibility. Finding natural representatives of a behaviour based on price flexibility is less easy, both because on early links the 11 production chains differ from one another and because in recent years many early stages of the production process have been moved abroad. Possibly, weavers are the best candidates, both because they are in the middle of production chains and because weaving technology is particularly simple to acquire so that traditionally there are many weavers, each of which is very small.

Let us introduce two other indicators: finishers' mobility and weavers' mobility. These indicators refer to particular finishers (weavers) included in the production chains built by a particular middleman over time steps, regardless of chain types.

Finishers' mobility and weavers' mobility are computed as follows. Firstly, persistence is calculated. This is the number of times that each particular finisher (weaver) has been attached to the same side of the same middleman. It is calculated over blocks of one thousand chains built during one year, except for the last block of each year. Block values are averaged in order to obtain yearly values denoted summedFinisherPersistence and summedWeaverPersistence, respectively. Finally, mobility is calculated as one minus the ratio of persistence to the number of chains that have been built in a year.

The higher the mobility of a firm, the higher the flexibility that it provides. Thus, if we assume that weavers mainly provide price flexibility and finishers mainly provide feature flexibility, we can observe the evolution of the relative importance of these two factors. Figure 9 plots finishers' mobility and weavers' mobility calculated by the 1:1 model and averaged over ten runs.

Figure 9. Mobility of Finishers and Weavers averaged over ten runs. Scale of the simulations: 1:1. Variance of the distribution that regulates the movements of traders of finished products: 10.0. Watching range of traders of finished products: 10x10 pixels. World size: 500x600 pixels.

In figure 9 we see that finishers' mobility and weavers' mobility were both very low when the district was in its infancy, meaning that there was little flexibility of any kind. The Golden Age of the 1960s and 1970s was characterised by high weavers' mobility and low finishers' mobility, indicating that the district was relying on price flexibility alone. However, the crisis decade of the 1980s already shows the seeds of the recovery of the 1990s, since finishers' mobility was slowly increasing. Finally, at the beginning of the 1990s finishers' mobility approached weavers' mobility, meaning that feature flexibility finally became just as important as price flexibility. Notably, price flexibility did not decrease in the 1980s and 1990s. Eventually, it increased a little, possibly because of massive clandestine immigration.

Interestingly, figure 9 does not show any sharp divide between the crisis of the 1980s and the recovery of the 1990s. Possibly, interviews concerning profits and expectations (Balestri and Toccafondi 1994, Balestri and Toccafondi 1995) show a sharper discontinuity than data on the number of firms, simply because a long time is needed in order for unprofitable, traditionally managed family firms to disappear from the market. Possibly, an economy where unprofitable firms immediately go bankrupt had experienced a sharper crisis and an earlier recovery.

The curves illustrated in figures 8 and 9 seem to be quite robust with respect to parameter values. In order to evaluate the sensitivity of the model to the variance of the distribution that regulates movements of the traders of finished products, to the watching range of the traders of finished products and to the size of the world where firms move, six series of five runs have been carried out. In these series, the above three parameters were either increased or decreased by 10%. Subsequently, for each parameter value the average of the five runs was compared with the average of five runs carried out with the base parameter values. Comparison was made by computing the average percentage of the absolute difference between a curve resulting from new parameter values and the corresponding curve resulting from base parameter values. In order to assess the role of chance differences, a similar comparison was made between two curves resulting from the average of two series of five runs with base parameters values. Table 1 illustrates the results.

Table 1. Indices of the impact of parameters variations on model outcomes. Given a curve {xi} obtained by averaging five runs with base parameters values and a curve {yi} obtained by averaging five runs with modified parameters values, the index is the average per cent of |yi-xi|/xi. In the case of the last column, the two series have been obtained by averaging two different series of five runs with base values

On the whole, the model appears to be very robust with respect to 10% variations of all three parameters. In particular, a 10% variation of variance appears not to have any impact beyond the difference that can be expected between any two series of five runs with base values of all parameters. The model is more sensitive to variations of the watching range of traders of finished products as well as to variations of world size, but still to a very limited extent. Among the curves, parallelism is the one that is most sensitive to parameter variations, possibly because it often takes very low values.

Model scale is not really a parameter, but rather a modelling strategy. Its effect is interesting because it shows whether large agent-based models are worth doing. Figures 10 and 11 compare the 1:1 model with the 1:10 model for variability and parallelism, finishers' mobility and weavers' mobility, respectively.

Figure 10. Variability and parallelism for the 1:1 model and the 1:10 model, averaged over ten runs

Figure 11. finishers' mobility and weavers' mobility for the 1:1 model and the 1:10 model, averaged over ten runs

In figure 10 we can see that both variability and parallelism in the 1:10 model are delayed with respect to variability and parallelism in the 1:1 model, but also that in the 1:10 model variability increases more steeply than in the 1:1 model. Thus, the 1:10 model does not show a long "Golden Age" period of high variability and low parallelism, not even a delayed one. In figure 11 we can see that finishers' mobility and weavers' mobility in the 1:10 model are not delayed compared with the 1:1 model, but they behave very differently in the final part of the simulation. Apparently, the 1:10 model is not able to capture the slight but continuous increase of price flexibility that took place in the 1980s and 1990s. Thus, it appears that working with real sizes is crucial for empirical agent-based models.

Concluding Remarks

This research was initiated by a suggestion of an economist to a physicist, that industrial districts could possibly be studied as self-organising systems. Ant-hills are a common metaphor for this kind of models, since the behaviour of an ant-hill is far more complex than the behaviour of any single ant. The idea was that, in some sense, an industrial district works like an ant-hill.

This idea had to be qualified in the course of the investigation, because the Pratese district appeared to have a structure of its own, centred around the figure of middlemen. As far as it concerns technology and aesthetical novelties, Prato is a self-organising system. However, to the extent that production is organised by middlemen, it is not self-organised. Essentially, self-organisation requires equal distribution of capabilities and power among reactive but simple components that establish a number of links with one another. This is not the case of Prato, since middlemen have entrepreneurial capabilities and acquaintances that other agents lack.

Possibly, we are bumping into a kind of general principle. The above analysis may suggest that the more intelligent the components, the less intelligent the whole. Do human societies exhibit a macroscopic intelligence of which we are unaware, just like neurones are unaware of the brain? If a little experience with a textile industrial district can be extrapolated to the whole of human society, the answer is "No". The human-hill may be less intelligent than the ant-hill.

Acknowledgements

This study is at odds with prevailing literature on Italian industrial districts, particularly in so far as it considers the importance of clandestine immigrants but also with respect to the role of middlemen. As such, it raised criticisms, enthusiastic comments and surprised remarks. Since all of them concurred to improve my paper, I am equally grateful to Peter Allen, Tito Arecchi, Alberto Baccini, Harald Bathelt, Marco Bellandi, Fiorenza Belussi, Lucio Biggiero, Gabi Dei Ottati, Paolo Giaccaria, Robert Hassink, Mauro Lombardi, Peter Maskell, Bart Nooteboom, Päivi Oinas, Antonio Politi, Fabio Sforzi, Flaminio Squazzoni, Deborah Tappi, Michael Taylor, Eirik Vatne, Alessandro Vercelli, Bauke Visser, Sieglinde Walter and Jici Wang. Furthermore, special thanks are due to Gianluigi Ferraris and Matteo Morini who provided patient and continuous help in writing the simulation program, Luciana Lazzeretti and Dimitri Storai who assembled a valuable database, Andrea Balestri of Unione Industriale Pratese who provided information on fabric variety, and particularly to Serafino Romeo of Pratese Caritas, who engaged in a quest for rare and valuable data. Finally, it is hard to say how much I feel indebted to the continuous help, assistance and, most importantly, encouragement and esteem of Pietro Terna, who sacrificed the honors of congress limelights in order to defend an uncomfortable paper.

Notes

1 In Pratese jargon these are the contoterzisti, meaning literally "workers for a third party" because they do not sell their products to the person who ordered them in the first place. Workers on contract, we would say.

2 In this case, Pratese jargon employs the specific word impannatori. It derives from panno, which means "cloth".

LOMBARDI M (2000) The Evolution of Local Production Systems: the emergence of the "invisible mind" and the evolutionary pressures towards more visible "minds". Paper presented at the Regional Enterprise Network Conference, Prague, 22-23 October.

LOMBARDI M (2001) "Cognitive equilibria, efficiency, and discontinuities in the evolution of Local Production Systems". In Belussi, F., Gottardi, G. and Rullani, E. (Eds.) Knowledge creation, learning, and variety of institutional arrangements, forthcoming.

WANG J, Zhu H and Tong X (2001) Districtization in the Zhejiang Province of China with Reference to Datang Socks/Stockings Industrial District. Paper presented at the Conference of the IGU Commission on the Dynamics of Economic Spaces, Turin, Italy, July 9-14.